Abstract : Certain crucial financial time series, such as the interconnected european electricity market spot prices, exhibit long memory, in the sense of slowly decaying correlations combined with heteroskedasticity and periodic or none cycles. In modeling such behavior, we consider on one hand, the k factor GIGARCH process and additionally propose two methods to address the related parameter estimation problem. In each method, we explore the asymptotic theory for estimation. Moreover, the asymptotic properties are validated and compared via Monte Carlo simulations. On the other hand, we introduce a new multivariate long memory generalized model kfactor MVGARMA in order to model interconnected european electricity market spot prices. We sugger a practical framework to address the parameter estimation problem. We investigate the analytical expressions of the least squares predictors for the two proposed models and their confidence intervals. To finish, we apply the two proposed models to the french and german electricity market spot prices and a comparison is made between their forecasting abilities.